We construct an effective low energy Hamiltonian which describes fermions dwelling on a deformed honeycomb lattice with dislocations and disclinations, and with an arbitrary hopping parameters of the corresponding tight binding model. It describes the interaction of fermions with a 2d gravity and has also a local SU(2) gauge invariance of the group of rotations. We reformulate the model as interaction of fermions with the deformation of the lattice, which forms a phonon field. We calculate the response of fermion currents to the external deformation or phonon field, which is a result of a Z_2 anomaly. This can be detected experimentally.
The Casimir force between two infinitely thin parallel sheets in a setting of $N$ such sheets is found. The finite two-dimensional conductivities, which describe the dispersive and absorptive properties of each sheet, are taken into account, whereupon the theory is applied to interacting graphenes. By exploring similarities with in-plane optical spectra for graphite, the conductivity of graphene is modeled as a combination of Lorentz type oscillators. We find that the graphene transparency and the existence of a universal constant conductivity $e^2/(4\hbar)$ result in graphene/graphene Casimir…
A thermal transport mechanism leading to the enhanced thermal conductivity of Graphene nanofluids has been proposed. The Graphene sheet size is postulated to be the key to the underlying mechanism. Based on a critical sheet size derived from Stokes-Einstein equation for the poly-dispersed nanofluid, sheet percolation and Brownian motion assisted sheet collisions are used to explain the heat conduction. A collision dependant dynamic conductivity considering Debye approximated volumetric specific heat due to phonon transport in Graphene has been incorporated. The model has been found to be in go…
We study an interface between two media separated by a strictly 2D sheet. We show how the amplitude reflection coefficient can be modeled by that for an interface where the 2D sheet has been replaced by a film of small but finite thickness. We give the relationship between the 3D dielectric function of the thin film and the 2D dielectric function of the sheet. We choose graphene and a 2D metallic sheet as illustrative examples. This approach turns out to be very useful when treating graphene or graphene like sheets in non-planar structures
Impact of induced strain on charge carrier mobility is investigated for a monolayer graphene sheet. Mobility is computed within Born approximation by including impurity scattering, surface roughness effects and interaction with lattice phonons. Unlike its sSi counterpart, strained graphene shows a drop in mobility with increasing strain. Main reason for this effect is decrease in Fermi velocity due to induced distortions in the graphene honeycomb.
We study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. Furthermore, the resistivity of wrinkled graphene sheets is calculated for different ave…
Large-scale atomically thin metals can be stabilized through confinement epitaxy at graphene / SiC interface, which exhibit a gradient bonding type and are air stable, providing a compelling platform for quantum and optoelectronic technologies.
We study the Casimir friction phenomenon in a system consisting of two flat, infinite, and parallel graphene sheets, which are coupled to the vacuum electromagnetic (EM) field. Those couplings are implemented, in the description we use, by means of specific terms in the effective action for the EM field. They incorporate the distinctive properties of graphene, as well as the relative sliding motion of the sheets. Based on this description, we evaluate two observables due to the same physical effect: the probability of vacuum decay and the frictional force. The system exhibits a threshold for f…
Considerable efforts have been made to trap massless Dirac fermions in graphene monolayer, but only quasi-bound states are realized in continuous graphene sheets up to now. Here, we demonstrate the realization of bound states in nanoscale graphene quantum dots (GQDs) in a continuous graphene sheet. The GQDs are electronically isolated from the surrounding continuous graphene sheet by circular boundaries, which are generated by strong coupling between graphene and substrate. By using scanning tunneling microscopy (STM), we observe single-electron charging states of the GQDs, seen as Coulomb osc…
The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may explain why one always observes a ripple structure on suspended graphene. We show that a compression-relaxation mechanism produces static ripples on graphene sheets and determine a peculiar temperature $T_c$, such that for $T<T_c$ the free-energy of the rippled graphene is smaller than that of roughened graphene. We also show that $T_c$ depends on the structur…
We present a study of the wrinkling modes, localized in the plane of single- and few-layer graphene sheets embedded in or placed on a compliant compressively strained matrix. We provide the analytical model based on nonlinear elasticity of the graphene sheet, which shows that the compressive surface stress results in spatial localization of the extended sinusoidal wrinkling mode with soliton-like envelope with localization length, decreasing with the overcritical external strain. The parameters of the extended sinusoidal wrinkling modes are found from the conditions of anomalous softening of f…
We present a calculation of the quasiparticle decay rate due to electron-electron interactions in a doped graphene sheet. In particular, we emphasize subtle differences between the perturbative calculation of this quantity in a doped graphene sheet and the corresponding one in ordinary parabolic-band two-dimensional (2D) electron liquids. In the random phase approximation, dynamical overscreening near the light cone yields a universal quasiparticle lifetime, which is independent of the dielectric environment surrounding the 2D massless Dirac fermion fluid.
We study the Landau levels in curved graphene sheets by measuring the discrete energy spectrum in the presence of a magnetic field. We observe that in rippled graphene sheets, the Landau energy levels satisfy the same square root dependence on the energy quantum number as in flat sheets, $E_n \sim \sqrt{n}$. Though, we find that the Landau levels in curved sheets are shifted towards lower energies by an amount proportional to the average spatial deformation of the sheet. Our findings are relevant for the quantum Hall effect in curved graphene sheets, which is directly related to Landau quantiz…
We elucidate on the low mobility and charge traps of the chemically reduced graphene oxide (RGO) sheets by measuring and analyzing temperature dependent current-voltage characteristics. The RGO sheets were assembled between source and drain electrodes via dielectrophoresis. At low bias voltage the conduction is Ohmic while at high bias voltage and low temperatures the conduction becomes space charge limited with an exponential distribution of traps. We estimate an average trap density of 1.75x10^16 cm^-3. Quantitative information about charge traps will help develop optimization strategies of …
Nonequilibrium molecular dynamics simulations is used to study the motion of a C60 molecule on a graphene sheet subjected to a temperature gradient. The C60 molecule is actuated and moves along the system while it just randomly dances along the perpendicular direction. Increasing the temperature gradient increases the directed velocity of C60. It is found that the free energy decreases as the C60 molecule moves toward the cold end. The driving mechanism based on the temperature gradient suggests the construction of nanoscale graphene-based motors.
The motion of a C60 molecule over a graphene sheet at finite temperature is investigated both theoretically and computationally. We show that a graphene sheet generates a van der Waals laterally periodic potential, which directly influences the motion of external objects in its proximity. The translational motion of a C60 molecule near a graphene sheet is found to be diffusive in the lateral directions. While, in the perpendicular direction, the motion may be described as diffusion in an effective harmonic potential which is determined from the distribution function of the position of the C60 …
Organic ferroelectric layers sandwiched between the graphene sheets are presented as a model of the solar cell. The investigated systems display many advantageous properties: 1) the cascade energy-levels alignment, 2) simultaneous donor and acceptor character depending on the charge-carrier direction, 3) the charge-transfer excitonic type, 4) the induced polarization of the electrodes, leading to a substantial work-function change of the anode and cathode - around +/-1.5 eV, respectively.
The orbital magnetic susceptibility (OMS) of a gas of noninteracting massless Dirac fermions is zero when the Fermi energy is away from the Dirac point. Making use of diagrammatic perturbation theory, we calculate exactly the OMS of massless Dirac fermions to first order in the Coulomb interaction demonstrating that it is finite and positive. Doped graphene sheets are thus unique systems in which the OMS is completely controlled by many-body effects.
Nanoindentation of bilayer graphene is studied using molecular dynamics simulations. We compared our simulation results with those from elasticity theory as based on the nonlinear Föppl-Hencky equations with rigid boundary condition. The force deflection values of bilayer graphene are compered to those of monolayer graphene. Young's modulus of bilayer graphene is estimated to be 0.8 TPa which is close to the value for graphite. Moreover, an almost flat bilayer membrane at low temperature under central load has a 14$%$ smaller Young's modulus as compared to the one at room temperature.
We study the dependence of mechanical conformations of graphene sheets located on flat substrates on the density of unilateral (one-side) attachment of hydrogen, fluorine or chlorine atoms to them. It is shown that chemically modified graphene sheet can take four main forms on a flat substrate: the form of a flat sheet located parallel to the surface of the substrate, the form of convex sheet partially detached from the substrate with bent edges adjacent to the substrate, and the forms of single and double rolls on the substrate. On the surface of crystalline graphite, the flat form of the she…
We investigate the propagation of surface waves along a spatially dispersive graphene sheet, including substrate effects. The proposed analysis derives the admittances of an equivalent circuit of graphene able to handle spatial dispersion, using a non-local model of graphene conductivity. Similar to frequency selective surfaces, the analytical admittances depend on the propagation constant of the waves traveling along the sheet. Dispersion relations for the supported TE and TM modes are then obtained by applying a transverse resonance equation. Application of the method demonstrates that spati…
We present the experimental evidence of RF demodulation by a graphene monolayer embedded in a coplanar structure. The demodulator was tested in the frequency range from 100 MHz to 25 GHz using amplitude modulated input signals. An input power of 0 dBm (1 mW) was used which is the typical power emitted for short range wireless communication systems, such as Bluetooth. The graphene demodulator exhibits good signal response in the frequency range associated to industrial, scientific and medical (ISM) radio band (2.4 GHz).
We formulate a nonlinear continuum model of a graphene sheet supported by a flat rigid substrate. The sheet is parallel to the substrate and loaded on a pair of opposite edges. A typical cross-section of the sheet is modeled as an elastica. We use elementary techniques from bifurcation theory to investigate how the buckling of the sheet depends on the boundary conditions, the composition of the substrate, and the length of the sheet. We also present numerical results that illustrate snap-buckling of the sheet.
Molecular dynamics (MD) simulations were performed to study the formation process of nanopores in a suspended graphene sheet irradiated by using energetic ions though a mask. By controlling the ion parameters including mass, energy and incident angle, different kinds of topography were observed in the graphene sheet. Net-like defective strucutures with carbon atom chains can be formed at low ion fluence, which provides the possibility to functionalize the irradiated sample with subsequent chemical methods; finally a perfect nanopore with smooth edge appears as the ion fluence is high enough. W…
Epitaxial graphene grown on SiC by the confinement controlled sublimation method is reviewed, with an emphasis on multilayer and monolayer epitaxial graphene on the carbon face of 4H-SiC and on directed and selectively grown structures under growth-arresting or growth-enhancing masks. Recent developments in the growth of templated graphene nanostructures are also presented, as exemplified by tens of micron long very well confined and isolated 20-40nm wide graphene ribbons. Scheme for large scale integration of ribbon arrays with Si wafer is also presented.
The quantum capacitance model is applied to obtain an exact solution for the space-resolved carrier density in a multigated doped graphene sheet at zero temperature, with quantum correction arising from the finite electron capacity of the graphene itself taken into account. The exact solution is demonstrated to be equivalent to the self-consistent Poisson-Dirac iteration method by showing an illustrative example, where multiple gates with irregular shapes and a nonuniform dopant concentration are considered. The solution therefore provides a fast and accurate way to compute spatially varying c…
An infinite sheet of graphene lying above a perturbed ground plane is studied. The perturbation is a two dimensional ridge, and a bias voltage is applied between the graphene and the ground plane, resulting in a graphene nanoribbonlike structure with a soft-boundary (SB) The spatial distribution of the graphene conductivity forming the soft-boundary is studied as a function of the ridge parameters and the bias voltage. The current distribution of the fundamental TM surface plasmon polariton (SPP) is considered. The effect of the ridge parameters and shape of the soft boundary on the current di…
We demonstrate that the one-dimensional (1D) transport channels that appear in the gap when graphene nanoroads are embedded in boron-nitride (BN) sheets are more robust when they are inserted at AB/BA grain boundaries. Our conclusions are based on ab-initio electronic structure calculations for a variety of different crystal orientations and bonding arrangements at the BN/C interfaces. This property is related to the valley-Hall conductivity present in the BN band structure and to the topologically protected kink states that appear in continuum Dirac models with position dependent masses.
We investigate the dependence of the thermal Casimir force between two graphene sheets on the drift velocity of the electrons in one graphene sheet. We show that the drift motion produces a measurable change of the thermal Casimir force due to the Doppler effect. The thermal Casimir force as well as the Casimir friction are strongly enhanced in the case of resonant photon tunneling when the energy of the emitted photon coincides with the energy of electron-hole pair excitations. In the case of resonant photon tunneling, even for temperatures above room temperature the Casimir friction is domin…
Optical extinction and absorption enhancement in the infrared range of a monolayer graphene sheet by patterning split ring resonators (SRRs) is studied. It is found that the electric mode is stronger in enhancing infrared extinction and absorption compared to the magnetic mode and other higher-order modes. We improve the infrared extinction of the SRR graphene sheet by increasing the graphene area ratio in the SRR unit cell design. With the increase of the graphene area ratio, the radiation ability of the electric dipolar mode and dissipation of graphene compete for a maximum infrared absorpti…
The extraordinary properties of graphene make it a very promising material for use in optoelectronics. However, this is still a nascent field, where some basic properties of the electromagnetic field in graphene must be explored. Here we report on the fields radiated by a nanoemitter lying on a graphene sheet. Our results show that this field presents a rich dependence on both frequency, distance to the source and dipole orientation. This behavior is attributed to distinct peculiarities on the density of electromagnetic states in the graphene sheet and the interaction between them. The field i…
We have carried out first-principles calculations on electronic properties of graphene quantum dots embedded in hexagonal boron nitride monolayer sheets. The calculations with density functional theory show that the band gaps of quantum dots are determined by the quantum confinement effects and the hybridization of π orbitals from B, N and C atoms. The energy states near the Fermi level are found to be strongly localized within and in the vicinity of the quantum dots.
We present a novel potential model for calculating the interaction between a molecule and a single graphene sheet. The dispersion/repulsion, induction, dipole-quadrupole, quadrupole-quadrupole interactions between a fluid molecule and a graphene sheet are described by integrated functions that are only dependent on the separation between the molecule and the graphene along its planar normal. The derived potential functions are in excellent agreement with the computationally demanding atom-explicit summation method. Typical errors of the integrated potential are less than 2% in the energy minim…
We study the effect of disordered ripples on the conductivity of monolayer graphene flakes. We calculate the relaxation times and the Boltzmann conductivities associated with two mechanisms. First, we study the conductivity correction due to an external in-plane magnetic field $B_\parallel$. Due to the irregular local curvature found at graphene sheets deposited over a substrate, $B_\parallel$ can be mapped into an effective random magnetic field perpendicular to the graphene surface. Second, we study the electron momentum relaxation due to intrinsic pseudo magnetic fields originated from defo…
On the basis of first principles calculations, we report energy estimated to cut a graphene sheet into nanoribbons of armchair and zigzag configurations. Our calculations show that the energy required to cut a graphene sheet into zigzag configuration is higher than that of armchair configuration by an order of 0.174 eV. Thus, a control over the threshold energy might be helpful in designing an experiment for cutting a graphene sheet into smooth edged armchair or zigzag configurations.
Excitation of surface plasmons supported by doped graphene sheets at terahertz frequencies is investigated numerically. To alleviate the momentum mismatch between the highly-confined plasmon modes and the incident radiation, it is proposed to increase the surface conductivity of graphene through high doping levels or with few-layer graphene. For currently achievable doping levels, our analysis shows that surface plasmons on monolayer graphene may be excited at operating frequencies up to about 10 THz (~ 41.3 meV) with a high-index coupling prism, and higher frequencies/energies are possible fo…
The Casimir force between graphene sheets is investigated with emphasis on the effect from spatial dispersion using a combination of factors, such as a nonzero chemical potential and an induced energy gap. We distinguish between two regimes for the interaction - T=0 $K$ and $T\neq 0$ $K$. It is found that the quantum mechanical interaction (T=0 $K$) retains its distance dependence regardless of the inclusion of dispersion. The spatial dispersion from the finite temperature Casimir force is found to contribute for the most part from $n=0$ Matsubara term. These effects become important as graphe…
The light-like dispersion of graphene monolayer results in many novel electronic properties in it1, however, this gapless feature also limits the applications of graphene monolayer in digital electronics2. A rare working solution to generate a moderate bandgap in graphene monolayer is to cut it into one-dimensional (1D) nanometre-wide ribbons3-13. Here we show that a wide bandgap can be created in a unique 1D strained structure, i.e., graphene-nanoribbon-like (GNR-like) structure, of a continuous graphene sheet via strong interaction between graphene and the metal substrate, instead of cutting…
Flexoelectricity phenomenon is the response of electric polarization to an applied strain gradient and is developed as a consequence of crystal symmetry in all materials. In this study, we show that the presence of strain gradient in non-piezoelectric graphene sheet does not only affect the ionic positions, but also the asymmetric redistribution of the electron density, which induce strong polarization in the graphene sheet. Using quantum mechanics calculations, the resulting axial and normal piezoelectric coefficients of the graphene sheet were determined using two loading conditions: (i) a g…
This erratum aims to correct 1) the wrong expressions, 2) some typographical errors, 3) some erroneous points made in discussion of the disparity of heat flux ratios between our full RPA model and the local conductivity model, and 4) the lower bound of the characteristic distance scale comparable to the graphene thermal length, appearing in the original paper, which might confuse or mislead readers. Collectively, they don't change the key physics we sought to present.
By using four-terminal configurations, we investigated the dependence of longitudinal and diagonal resistances of a graphene p-n interface on the quantum-Hall edge-state equilibration position. The resistance of a p-n device in our four-terminal scheme is asymmetric with respect to the zero point where the filling factor ($ν$) of the entire graphene vanishes. This resistance asymmetry is caused by the chiral-direction-dependent change of the equilibration position and leads to a deeper insight into the equilibration process of the quantum-Hall edge states in a bipolar graphene system.
First principle calculations of the phonons of graphene-BN heterostructures are presented and compared to those of the constituents. We show that AA and AB' stacking are not only energetically less favoured than AB but also dynamically unstable. We have identified low energy flat phonon branches of BN character with out of plane displacement and evaluated their coupling to electrons in graphene.
Using typical experimental techniques it is difficult to separate the effects of carrier density and disorder on the superconducting transition in two dimensions. Using a simple fabrication procedure based on metal layer dewetting, we have produced graphene sheets decorated with a non-percolating network of nanoscale tin clusters. These metal clusters both efficiently dope the graphene substrate and induce long-range superconducting correlations. This allows us to study the superconducting transition at fixed disorder and variable carrier concentration. We find that despite structural inhomoge…
Constrained density functional theory (CDFT) is used to evaluate the energy level alignment of a benzene molecule as it approaches a graphene sheet. Within CDFT the problem is conveniently mapped onto evaluating total energy differences between different charge-separated states, and it does not consist in determining a quasi-particle spectrum. We demonstrate that the simple local density approximation provides a good description of the level aligmnent along the entire binding curve, with excellent agreement to experiments at an infinite separation and to GW calculations close to the bonding di…
We calculate hybridization of plasmons and intrinsic optical phonons in graphene by using the self-consistent linear response formalism. We find that longitudinal plasmons (transverse magnetic modes) couple exclusively to transverse optical phonons, whereas graphene's transverse plasmons (transverse electric modes) couple only to longitudinal optical phonons. This mixing of polarizations is in contrast to the usual plasmon-phonon coupling in other systems. The resulting change in phonon frequencies increases (decreases) for transverse (longitudinal) phonons by increasing the concentration of c…
The interlayer gallery between two adjacent sheets of van der Waals materials is expected to modify properties of atoms and molecules confined at the atomic interfaces. Here, we directly image individual hydrogen atom intercalated between two graphene sheets and investigate its dynamics by scanning tunnelling microscope (STM). The intercalated hydrogen atom is found to be remarkably different from atomic hydrogen chemisorbed on external surface of graphene. Our STM measurements, complemented by first-principles calculations, show that the hydrogen atom intercalated between two graphene sheets …
We derive an integral equation describing surface-plasmon polaritons in graphene deposited on a substrate with a planar surface and a dielectric protrusion in the opposite surface of the dielectric slab. We show that the problem is mathematically equivalent to the solution of a Fredholm equation, which we solve exactly. In addition, we show that the dispersion relation of the localized surface plasmons is determined by the geometric parameters of the protrusion alone. We also show that such system supports both even and odd modes. We give the electrostatic potential and the stream plot of the …
We report on the fabrication and operation of a multi-element vibrational structure consisting of two graphene mechanical resonators coupled by a nanotube beam. The whole structure is suspended. Each graphene resonator is clamped by two metal electrodes. The structure is fabricated using a combination of electron-beam lithography and atomic-force microscopy nano-manipulation. This layout allows us to detect the mechanical vibrations electrically. The measured eigenmodes are localized in either one of the graphene resonators. The coupling due to the nanotube is studied by measuring the shift of…
We find analytic asymptotic expressions at low temperature for the Casimir free energy, entropy and pressure of two parallel graphene sheets in the framework of the Lifshitz theory. The reflection coefficients of electromagnetic waves on graphene are described on the basis of first principles of quantum electrodynamics at nonzero temperature using the polarization tensor in (2+1)-dimensional space-time. The leading contributions to the Casimir entropy and to the thermal corrections to the Casimir energy and pressure are given by the thermal correction to the polarization tensor at nonzero Mats…
The thermal free energy and pressure of dispersion interaction between two graphene sheets described by the Dirac model are calculated using the Lifshitz formula with reflection coefficients expressed via the polarization tensor. The obtained results for a pristine graphene are found to be in agreement with computations using Coulomb coupling between density fluctuations. For a graphene with nonzero mass gap parameter a qualitatively different behavior for the free energy and pressure is obtained. The Lifshitz formula with reflection coefficients expressed via the polarization tensor is used a…
